Midterm Project: Effects of Air Pollution on Countries

1. Introduction

Motivation

Climate issues are pervasive but typically disproportionately affect low income communities and developing countries. Our group wanted to explore how air pollution has changed over time and affect countries differently. Specifically, we wanted to analyze how a country’s economic and social position can either increase, decrease, or not have observable impact on the affects of air pollution. In laymen terms, does air pollution affect underdeveloped countries disproportionately?

Set Up

Before we start, we need to ensure that we have all the relevant libraries installed and imported.

Run these in the console, or only the ones that your system does not have, to install packages in addition to the ezids package.

install.packages("tidyverse")
install.packages("rworldmap")
install.packages("tmap")
install.packages("spData")
install.packages("sf")
install.packages("ggpubr")
install.packages("dplyr")
install.packages("knitr")
install.packages("magrittr")

2. Data Sources and Data Wrangling

Data Sources

For our analysis, we will be working with 5 main data sources shown in the table below:

Figure 1: Data Sources
Data	Source	Link
Deaths Due to Air Pollution of Countries from 1990 - 2017	Kaggle	Link
GDP Annual Growth of Countries from 1960 - 2020	Kaggle via WorldBank	Link
United Nations Population and Region Data	United Nations	Link
United Nations ISO-alpha3 code	United Nations	Link
spData for Map Geometries	spData for Mapping	Link

The main variables in our datasets will include:

Figure 2: Key Variables
Feature	Data Type	Unit of Measure	Notes and Assumptions
GDP (Gross Domestic Product)	Numerical, Continuous	$USD	This is our chosen proxy for measuring a country’s economic status
Population Size	Numerical, Continuous	thousands of people	Annual UN estimated
Deaths due to Air Pollution	Numerical, Continuous	deaths per million	This is our chosen proxy for measuring the negative affects of air pollution.
Country	Qualitative, Categorical	N/A	231 countries
SDG Region	Qualitative, Categorical	N/A	UN’s Sustainable Development Goals Region Classification.
Sub Region	Qualitative, Categorical	N/A	UN’s Sustainable Development Goals Sub-Region Classification.
ISO-alpha3 Country Code	Qualitative, Categorical	N/A	Standard for identifying countries (text ID).
ISO-alpha2 Country Code	Qualitative, Categorical	N/A	Another standard for identifying countries (text ID).
M49 Country Code	Numerical, Categorical	N/A	Another standard for identifying countries (numerical ID).
Year	Numerical, Categorical	N/A	1990 to 2017
GDP per Capita	Numerical, Continuous	$USD per person	Normalization of GDP to compare between population sizes (calculated).

Data Wrangling

While data from Kaggle are already in a format to be cleaned, downloaded data from United Nations required a little data wrangling. Mainly, we needed to extract just countries’ data from the Excel workbooks and into their own contained csv files. Since we only need to do this once and programming it would take significant time to choose the specific cells that we need, we opted to perform this step outside of R and in Excel. Note that if this were a part of a real production data pipeline, we would take the time to program the data extraction but would likely choose a different programming language such as Python that is a bit more robust in these types of tasks like web scraping and data transformations in Pandas.

: Figure 3: Sample screenshot of data downloaded from UN including unnecessary elements like banners and other regional data.
: Figure 4: Sample screenshot of transformed UN dataset.

3. Load, Clean, and Inspect Data

Load Data

Figure 5: Structure of country_codes_df
variable	class	first_values
Country.or.Area	character	Andorra, United Arab Emirates (the), Afghanistan, Antigua and Barbuda, Anguilla, Albania
ISO.alpha2.code	character	AD, AE, AF, AG, AI, AL
ISO.alpha3.code	character	AND, ARE, AFG, ATG, AIA, ALB
M49.code	integer	20, 784, 4, 28, 660, 8

Figure 6: Structure of air_pollution_df
variable	class	first_values
Entity	character	Afghanistan, Afghanistan, Afghanistan, Afghanistan, Afghanistan, Afghanistan
Code	character	AFG, AFG, AFG, AFG, AFG, AFG
Year	integer	1990, 1991, 1992, 1993, 1994, 1995
Air.pollution..total…deaths.per.100.000.	double	299.477308883281, 291.277966734046, 278.963055615066, 278.790814746341, 287.162923177255, 288.01422374243
Indoor.air.pollution..deaths.per.100.000.	double	250.362909742375, 242.575124973334, 232.043877894811, 231.648133503794, 238.837176822107, 239.906598716878
Outdoor.particulate.matter..deaths.per.100.000.	double	46.4465894382846, 46.0338405670284, 44.2437660321924, 44.4401481443785, 45.5943284100213, 45.3671411300974
Outdoor.ozone.pollution..deaths.per.100.000.	double	5.61644203074918, 5.60396011603667, 5.61182206482564, 5.65526606275628, 5.71892222061506, 5.73917378233707

Figure 7: Structure of gdp_df, not showing all years in table to retain space but years go up to X2020
variable	class	first_values
Country.Name	character	Aruba, Afghanistan, Angola, Albania, Andorra, Arab World
Country.Code	character	ABW, AFG, AGO, ALB, AND, ARB
Indicator.Name	character	GDP (current US$), GDP (current US$), GDP (current US$), GDP (current US$), GDP (current US$), GDP (current US$)
Indicator.Code	character	NY.GDP.MKTP.CD, NY.GDP.MKTP.CD, NY.GDP.MKTP.CD, NY.GDP.MKTP.CD, NY.GDP.MKTP.CD, NY.GDP.MKTP.CD
X1960	double	NA, 537777811.111111, NA, NA, NA, NA
X1961	double	NA, 548888895.555556, NA, NA, NA, NA
X1962	double	NA, 546666677.777778, NA, NA, NA, NA
X1963	double	NA, 751111191.111111, NA, NA, NA, NA
X1964	double	NA, 800000044.444444, NA, NA, NA, NA
X1965	double	NA, 1006666637.77778, NA, NA, NA, NA

Figure 8: Structure of population_region_df, not showing all years in table to retain space but years go up to X2020
variable	class	first_values
SDGRegion	character	SUB-SAHARAN AFRICA, SUB-SAHARAN AFRICA, SUB-SAHARAN AFRICA, SUB-SAHARAN AFRICA, SUB-SAHARAN AFRICA, SUB-SAHARAN AFRICA
SubRegion	character	Eastern Africa, Eastern Africa, Eastern Africa, Eastern Africa, Eastern Africa, Eastern Africa
Country	character	Burundi, Comoros, Djibouti, Eritrea, Ethiopia, Kenya
Notes	integer	NA, NA, NA, NA, NA, NA
Country.code	integer	108, 174, 262, 232, 231, 404
Type	character	Country/Area, Country/Area, Country/Area, Country/Area, Country/Area, Country/Area
Parent.code	integer	910, 910, 910, 910, 910, 910
X1950	character	2 309, 159, 62, 822, 18 128, 6 077
X1951	character	2 360, 163, 63, 835, 18 467, 6 242
X1952	character	2 406, 167, 65, 849, 18 820, 6 416

Figure 9: Structure of world, not showing geom feature in table as it has unique list of values per row and therefore is extremely large to display.
variable	class	first_values
iso_a2	character	FJ, TZ, EH, CA, US, KZ
name_long	character	Fiji, Tanzania, Western Sahara, Canada, United States, Kazakhstan
continent	character	Oceania, Africa, Africa, North America, North America, Asia
region_un	character	Oceania, Africa, Africa, Americas, Americas, Asia
subregion	character	Melanesia, Eastern Africa, Northern Africa, Northern America, Northern America, Central Asia
type	character	Sovereign country, Sovereign country, Indeterminate, Sovereign country, Country, Sovereign country
area_km2	double	19289.9707329765, 932745.792357074, 96270.6010408472, 10036042.9767873, 9510743.74482458, 2729810.51298781
pop	double	885806, 52234869, NA, 35535348, 318622525, 17288285
lifeExp	double	69.96, 64.163, NA, 81.9530487804878, 78.8414634146341, 71.62
gdpPercap	double	8222.25378436842, 2402.09940362843, NA, 43079.1425247165, 51921.9846391384, 23587.3375151466

Clean Data

First thing that we need to drop unnecessary columns and set datatypes (factor, num, etc.).

Clean air_pollution_df:

Figure 10: Structure of air_pollution_df_cleaned
variable	class	first_values
Country	integer	Afghanistan, Afghanistan, Afghanistan, Afghanistan, Afghanistan, Afghanistan
ISO.alpha3.code	integer	AFG, AFG, AFG, AFG, AFG, AFG
Year	integer	1990, 1991, 1992, 1993, 1994, 1995
Deaths.Air.Pollution.per.100k	double	299.477308883281, 291.277966734046, 278.963055615066, 278.790814746341, 287.162923177255, 288.01422374243

Clean gdp_df:

Figure 11: Structure of gdp_df_cleaned
variable	class	first_values
Country	integer	Aruba, Aruba, Aruba, Aruba, Aruba, Aruba
ISO.alpha3.code	integer	ABW, ABW, ABW, ABW, ABW, ABW
Year	integer	1986, 1987, 1988, 1989, 1990, 1991
GDP.USD	double	405463417.11746, 487602457.746416, 596423607.114715, 695304363.031101, 764887117.194486, 872138715.083799

Clean population_region_df:

Figure 12: Structure of population_region_df_cleaned
variable	class	first_values
SDGRegion	integer	SUB-SAHARANAFRICA, SUB-SAHARANAFRICA, SUB-SAHARANAFRICA, SUB-SAHARANAFRICA, SUB-SAHARANAFRICA, SUB-SAHARANAFRICA
SubRegion	integer	EasternAfrica, EasternAfrica, EasternAfrica, EasternAfrica, EasternAfrica, EasternAfrica
Country	integer	Burundi, Burundi, Burundi, Burundi, Burundi, Burundi
M49.code	integer	108, 108, 108, 108, 108, 108
Year	integer	1950, 1951, 1952, 1953, 1954, 1955
Population.thousands	double	2309, 2360, 2406, 2449, 2492, 2537

Clean population_region_df:

Figure 13: Structure of country_codes_df
variable	class	first_values
Country.or.Area	integer	Andorra, United Arab Emirates (the), Afghanistan, Antigua and Barbuda, Anguilla, Albania
ISO.alpha2.code	integer	AD, AE, AF, AG, AI, AL
ISO.alpha3.code	integer	AND, ARE, AFG, ATG, AIA, ALB
M49.code	integer	20, 784, 4, 28, 660, 8

Clean world:

Figure 14: Structure of world_df_cleaned, not showing geom feature in table as it has unique list of values per row and therefore is extremely large to display.
variable	class	first_values
iso_a2	integer	FJ, TZ, EH, CA, US, KZ

Note that we only have geometries for 175 countries, some will not be able to be plot on a map but that is okay.

Final DataFrame Construction

Now let’s merge our 4 datasets into one using a series of inner joins using country code and year as keys depending on the specific join. We are using inner joins because we want to drop all null values which would mean either a country does not have a country code or we have more years of data than our smallest year range (the air pollution dataset).

Figure 15: Structure of final_df
variable	class	first_values
ISO.alpha2.code	integer	AD, AD, AD, AD, AD, AD
M49.code	integer	20, 20, 20, 20, 20, 20
Year	integer	2012, 2013, 1990, 1991, 1992, 1993
ISO.alpha3.code	integer	AND, AND, AND, AND, AND, AND
Country.x	integer	Andorra, Andorra, Andorra, Andorra, Andorra, Andorra
Deaths.Air.Pollution.per.100k	double	17.6754871826169, 17.1893417774086, 29.0238806202567, 28.6956788863825, 28.4603211317312, 27.8408717612189
GDP.USD	double	3188808942.56713, 3193704343.20627, 1029048481.88051, 1106928582.86629, 1210013651.87713, 1007025755.00065
SDGRegion	integer	EUROPE, EUROPE, EUROPE, EUROPE, EUROPE, EUROPE
SubRegion	integer	SouthernEurope, SouthernEurope, SouthernEurope, SouthernEurope, SouthernEurope, SouthernEurope
Population.thousands	double	82, 81, 55, 57, 59, 61
geom	list	list(), list(), list(), list(), list(), list()
gdp.per.capita	double	38887913.9337455, 39428448.6815589, 18709972.3978275, 19419799.6994086, 20508705.9640192, 16508618.9344369

Our dataset is finally ready to be analyzed.

4. EDA - Exploratory Data Analysis

Quick Plots

Let’s start our EDA process by just looking at some quick plots to look at the distribution of data.

Histogram of Air Pollution Induced Deaths, Population, and GDP per Capita

: Figure 16: Histogram of Air Pollution Induced Deaths per 100k.
: Figure 17: Histogram of Population.
: Figure 18: Histogram of GDP per Capita.

Looks like deaths.air.pollution.per.100k, population, and gdp.per.capita are not normal and are all right skewed.

Boxplot of Air Pollution Induced Deaths, Population, and GDP per Capita

Let’s look at a boxplot for the outliers.

: Figure 19: Boxplot of Deaths per 100,000 from Air Pollution vs SDG Region

Interesting to note that Australia/New Zealand, Europe, North America seem to have the lowest deaths per 100k from air pollution and are all fairly compactly packed together (low variance) relative to other regions around the world. Furthermore, these region contain the most advanced countries.

Let’s take another look but at SubRegions.

: Figure 20: Boxplot of Deaths per 100k from Air Pollution vs Sub Region

Separating out into an even granular grouping of regions show some trends where Australia/New Zealand, North America, Northern Europe, and Western Europe all have low deaths per 100k and have low variance. Historically, these regions consist of countries that have been considered ‘First World’ before our first year of analysis of 1990. We will dig into this more later in our SMART questions.

What does the GDP per capita of these regions look like comparatively? Let’s take a look.

: Figure 21: Boxplot of GDP per Capita vs Sub Region

Interesting to observe that the same subregions that have low deaths caused by air pollution also have high GDP per capita comparatively. We will try to see if we can quantify this relationship later on in our main research analysis.

Map of Countries

Due to the nature of our data set, plotting maps and maps with intensities can add another dimension to how we visualize and therefore understand our data.

: Figure 22: Global Map of SDGRegions and SubRegions
: Figure 23: Global Intensity Map of Key Numerical Features, 1990 to 2017

Looks like some inverse correlation between gdp.per.capita and deaths.air.pollution.per.100k.

We can also use ggplot2 to have a bit more control over map plotting.

: Figure 24: Global Intensity Map of Deaths due to Air Pollution per 100k People, 1990 to 2017
: Figure 25: Intensity Map of Deaths due to Air Pollution per 100k People in East and Southeastern Asia, 2017

SMART Questions

1. Is there a relationship between population size and Deaths per 100,000 due to air pollution?

Below, we would like to measure the relationship between Population size (in thousands) and Deaths per 100,000 due to air pollution. Since these variables are numerical, we have to confirm the normal distribution of both variables, and from the results below, we see that there is no correlation between a country’s population size and their deaths due to air pollution. we do observe a negative correlation between Deaths due to air pollution and GDP per Capita.

## 'data.frame':    5197 obs. of  12 variables:
##  $ ISO.alpha2.code              : Factor w/ 248 levels "AD","AE","AF",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ M49.code                     : Factor w/ 249 levels "4","8","10","12",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Year                         : Factor w/ 28 levels "1990","1991",..: 23 24 1 2 3 4 5 6 7 8 ...
##  $ ISO.alpha3.code              : Factor w/ 197 levels "","AFG","AGO",..: 5 5 5 5 5 5 5 5 5 5 ...
##  $ Country.x                    : Factor w/ 231 levels "Afghanistan",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Deaths.Air.Pollution.per.100k: num  17.7 17.2 29 28.7 28.5 ...
##  $ GDP.USD                      : num  3188808943 3193704343 1029048482 1106928583 1210013652 ...
##  $ SDGRegion                    : Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 4 4 4 4 4 4 4 4 4 4 ...
##  $ SubRegion                    : Factor w/ 22 levels "AUSTRALIA/NEWZEALAND",..: 19 19 19 19 19 19 19 19 19 19 ...
##  $ Population.thousands         : num  82 81 55 57 59 61 63 64 64 64 ...
##  $ geom                         :sfc_MULTIPOLYGON of length 5197; first list element:  list()
##   ..- attr(*, "class")= chr [1:3] "XY" "MULTIPOLYGON" "sfg"
##  $ gdp.per.capita               : num  38887914 39428449 18709972 19419800 20508706 ...

## [1] 0.037

##                               Deaths.Air.Pollution.per.100k
## Deaths.Air.Pollution.per.100k                         1.000
## Population.thousands                                  0.069
## gdp.per.capita                                       -0.543
##                               Population.thousands gdp.per.capita
## Deaths.Air.Pollution.per.100k                0.069         -0.543
## Population.thousands                         1.000         -0.040
## gdp.per.capita                              -0.040          1.000

Table
	Deaths.Air.Pollution.per.100k	Population.thousands	gdp.per.capita
Deaths.Air.Pollution.per.100k	1.000	0.069	-0.543
Population.thousands	0.069	1.000	-0.040
gdp.per.capita	-0.543	-0.040	1.000

2. Which countries had the highest and lowest deaths due to air pollution from 1990 - 2017? How is this related to the region?

## grouped_df [193 × 3] (S3: grouped_df/tbl_df/tbl/data.frame)
##  $ SDGRegion: Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 1 1 2 2 2 2 2 2 2 2 ...
##  $ Country.x: Factor w/ 231 levels "Afghanistan",..: 12 144 1 17 24 96 98 106 110 126 ...
##  $ total    : num [1:193] 498 446 3644 4046 3245 ...
##  - attr(*, "groups")= tibble [9 × 2] (S3: tbl_df/tbl/data.frame)
##   ..$ SDGRegion: Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 1 2 3 4 5 6 7 8 9
##   ..$ .rows    : list<int> [1:9] 
##   .. ..$ : int [1:2] 1 2
##   .. ..$ : int [1:14] 3 4 5 6 7 8 9 10 11 12 ...
##   .. ..$ : int [1:15] 17 18 19 20 21 22 23 24 25 26 ...
##   .. ..$ : int [1:40] 32 33 34 35 36 37 38 39 40 41 ...
##   .. ..$ : int [1:34] 72 73 74 75 76 77 78 79 80 81 ...
##   .. ..$ : int [1:24] 106 107 108 109 110 111 112 113 114 115 ...
##   .. ..$ : int [1:4] 130 131 132 133
##   .. ..$ : int [1:12] 134 135 136 137 138 139 140 141 142 143 ...
##   .. ..$ : int [1:48] 146 147 148 149 150 151 152 153 154 155 ...
##   .. ..@ ptype: int(0) 
##   ..- attr(*, ".drop")= logi TRUE

## Classes 'data.table' and 'data.frame':   10 obs. of  3 variables:
##  $ SDGRegion: Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 9 9 9 9 3 9 8 9 9 8
##  $ Country.x: Factor w/ 231 levels "Afghanistan",..: 85 123 179 32 111 86 183 38 141 159
##  $ total    : num  5109 5218 5240 5386 5425 ...
##  - attr(*, ".internal.selfref")=<externalptr> 
##  - attr(*, "sorted")= chr "total"

## Classes 'data.table' and 'data.frame':   10 obs. of  3 variables:
##  $ SDGRegion: Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 9 4 1 4 4 3 1 7 4 5
##  $ Country.x: Factor w/ 231 levels "Afghanistan",..: 184 199 144 95 73 104 12 35 74 219
##  $ total    : num  233 440 446 462 466 ...
##  - attr(*, ".internal.selfref")=<externalptr> 
##  - attr(*, "sorted")= chr "total"

3. Which regions have the lowest and highest deaths due to air pollution?

## grouped_df [252 × 3] (S3: grouped_df/tbl_df/tbl/data.frame)
##  $ SDGRegion: Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Year     : Factor w/ 28 levels "1990","1991",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ total    : num [1:252] 50.5 49.1 48.9 47.3 45.9 ...
##  - attr(*, "groups")= tibble [9 × 2] (S3: tbl_df/tbl/data.frame)
##   ..$ SDGRegion: Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 1 2 3 4 5 6 7 8 9
##   ..$ .rows    : list<int> [1:9] 
##   .. ..$ : int [1:28] 1 2 3 4 5 6 7 8 9 10 ...
##   .. ..$ : int [1:28] 29 30 31 32 33 34 35 36 37 38 ...
##   .. ..$ : int [1:28] 57 58 59 60 61 62 63 64 65 66 ...
##   .. ..$ : int [1:28] 85 86 87 88 89 90 91 92 93 94 ...
##   .. ..$ : int [1:28] 113 114 115 116 117 118 119 120 121 122 ...
##   .. ..$ : int [1:28] 141 142 143 144 145 146 147 148 149 150 ...
##   .. ..$ : int [1:28] 169 170 171 172 173 174 175 176 177 178 ...
##   .. ..$ : int [1:28] 197 198 199 200 201 202 203 204 205 206 ...
##   .. ..$ : int [1:28] 225 226 227 228 229 230 231 232 233 234 ...
##   .. ..@ ptype: int(0) 
##   ..- attr(*, ".drop")= logi TRUE

4. How does deaths due to air pollution increase over time? More specifically, are death rates in recent X amount of years higher than death rates from groups of X years before?

5. Main Research Question

Do lower GDP countries have more deaths per 100k due to air pollution?

Is there a correlation between GDP per capita and deaths caused by pollution? Is it linear? How strong is the correlation?

Linear Fit

Let’s first look at the general fit on the overall data.

: Figure XX: Linear model (fit1) on overall data, deaths due to air pollution per 100k vs GDP per capita, 1990 to 2017.

From the plot, we observe that there is indeed a negative correlation between deaths due to air pollution per 100k and GDP per capita. However, the strength of that relationship is not particularly strong as the R² is really low at 0.295. This means that only 29% of the variance experienced in deaths due to air pollution per 100k is caused by GDP per capita in a linear relationship.

Even looking at each individual SDGRegion, their linear fits get better overall but are still not particularly strong with the highest being Australia/New Zealand and Europe at R² of 0.56 and 0.55 respectively.

: Figure XX: Linear models for each SDGRegion, deaths due to air pollution per 100k vs GDP per capita, 1990 - 2017.

Let’s now look at how slicing by annual changes plays a part. : Figure XX: Linear models for each Year, deaths due to air pollution per 100k vs GDP per capita, 1990 - 2017.

As observed, time does not seem to play a significant part in describing the relationship between deaths due to air pollution per 100k vs GDP per capita as the R² stays roughly constant around 0.3 across all the years.

Transformed Log Scale - Linear Fit

Perhaps we should look at a non-linear fit. From our visuals, we see that every plot starts off at really high deaths due to air pollution per 100k then drops off dramatically as GDP per capita increases. However, the drop off begins to tamper off and asymptotically approaches some value. (It will be interesting to see if we can generalize what that GDP per capita value is. Let’s table that for later.) We have seen this type of behavior before in log graphs such as one shown below.

: Figure XX: Sample log graph.

Our data seems to be a -log(x) instead of log(x). Let’s transform our linear fit to a log fit by wrapping our features into a log() function and fitting back to a linear fit and see what the relationship is.

fit2’s summary statistics are:

## 
## Call:
## lm(formula = log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita), 
##     data = final_df_sf)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -1.099 -0.235  0.000  0.206  1.431 
## 
## Coefficients:
##                     Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)         10.07849    0.04871     207 <0.0000000000000002 ***
## log(gdp.per.capita) -0.38952    0.00323    -121 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.369 on 5195 degrees of freedom
## Multiple R-squared:  0.737,  Adjusted R-squared:  0.737 
## F-statistic: 1.45e+04 on 1 and 5195 DF,  p-value: <0.0000000000000002

Let’s replot with this new fit.

: Figure XX Fitting to a log(y) = (m)(log(x)) + b curve yields much stronger relationship by SDGRegion.
: Figure XX Fitting to a log(y) = (m)(log(x)) + b curve yields much stronger relationship by years.
: Figure XX Fitting to a log(y) = (m)(log(x)) + b curve yields much stronger relationship.

Across the board, the strength of our linear relationship increases dramatically when first transforming both features by the log() function first. The new R² is now 0.737 which means around 74% of the variance in our target feature can be explained by this mathematical relationship.

Let’s test a few more regression models by adding more features and see what happens.

fit3 <- lm(log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita)*SubRegion, data=final_df_sf)
fit4 <- lm(log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita)*SubRegion+Year, data=final_df_sf)
fit5 <- lm(log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita)*Year, data=final_df_sf)

R² values for adding more features are in fit3, fit4, and fit5 are 0.883, 0.887, and 0.747 respectively.

Let’s check out the VIFs to see if we should keep any of our new models.

Figure XX: VIF of lm(log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita)*SubRegion+Year
log(gdp.per.capita)	log(gdp.per.capita):SubRegionCaribbean	log(gdp.per.capita):SubRegionCentralAmerica	log(gdp.per.capita):SubRegionCentralAsia	log(gdp.per.capita):SubRegionEasternAfrica	log(gdp.per.capita):SubRegionEasternAsia	log(gdp.per.capita):SubRegionEasternEurope	log(gdp.per.capita):SubRegionMelanesia	log(gdp.per.capita):SubRegionMicronesia	log(gdp.per.capita):SubRegionMiddleAfrica	log(gdp.per.capita):SubRegionNorthernAfrica	log(gdp.per.capita):SubRegionNORTHERNAMERICA	log(gdp.per.capita):SubRegionNorthernEurope	log(gdp.per.capita):SubRegionPolynesia	log(gdp.per.capita):SubRegionSouth-EasternAsia	log(gdp.per.capita):SubRegionSouthAmerica	log(gdp.per.capita):SubRegionSouthernAfrica	log(gdp.per.capita):SubRegionSouthernAsia	log(gdp.per.capita):SubRegionSouthernEurope	log(gdp.per.capita):SubRegionWesternAfrica	log(gdp.per.capita):SubRegionWesternAsia	log(gdp.per.capita):SubRegionWesternEurope	SubRegionCaribbean	SubRegionCentralAmerica	SubRegionCentralAsia	SubRegionEasternAfrica	SubRegionEasternAsia	SubRegionEasternEurope	SubRegionMelanesia	SubRegionMicronesia	SubRegionMiddleAfrica	SubRegionNorthernAfrica	SubRegionNORTHERNAMERICA	SubRegionNorthernEurope	SubRegionPolynesia	SubRegionSouth-EasternAsia	SubRegionSouthAmerica	SubRegionSouthernAfrica	SubRegionSouthernAsia	SubRegionSouthernEurope	SubRegionWesternAfrica	SubRegionWesternAsia	SubRegionWesternEurope
975	7945	5044	3147	9101	2492	5911	2988	2640	5154	3892	3611	5909	1944	5987	7157	3933	5166	7168	9144	9611	5771	6747	3902	2131	5646	2101	4744	2281	2106	3457	2936	3714	5880	1584	4427	5680	3037	3437	6334	5707	8049	5965

Figure XX: VIF of lm(log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita)*SubRegion+Year.
log(gdp.per.capita)	log(gdp.per.capita):SubRegionCaribbean	log(gdp.per.capita):SubRegionCentralAmerica	log(gdp.per.capita):SubRegionCentralAsia	log(gdp.per.capita):SubRegionEasternAfrica	log(gdp.per.capita):SubRegionEasternAsia	log(gdp.per.capita):SubRegionEasternEurope	log(gdp.per.capita):SubRegionMelanesia	log(gdp.per.capita):SubRegionMicronesia	log(gdp.per.capita):SubRegionMiddleAfrica	log(gdp.per.capita):SubRegionNorthernAfrica	log(gdp.per.capita):SubRegionNORTHERNAMERICA	log(gdp.per.capita):SubRegionNorthernEurope	log(gdp.per.capita):SubRegionPolynesia	log(gdp.per.capita):SubRegionSouth-EasternAsia	log(gdp.per.capita):SubRegionSouthAmerica	log(gdp.per.capita):SubRegionSouthernAfrica	log(gdp.per.capita):SubRegionSouthernAsia	log(gdp.per.capita):SubRegionSouthernEurope	log(gdp.per.capita):SubRegionWesternAfrica	log(gdp.per.capita):SubRegionWesternAsia	log(gdp.per.capita):SubRegionWesternEurope	SubRegionCaribbean	SubRegionCentralAmerica	SubRegionCentralAsia	SubRegionEasternAfrica	SubRegionEasternAsia	SubRegionEasternEurope	SubRegionMelanesia	SubRegionMicronesia	SubRegionMiddleAfrica	SubRegionNorthernAfrica	SubRegionNORTHERNAMERICA	SubRegionNorthernEurope	SubRegionPolynesia	SubRegionSouth-EasternAsia	SubRegionSouthAmerica	SubRegionSouthernAfrica	SubRegionSouthernAsia	SubRegionSouthernEurope	SubRegionWesternAfrica	SubRegionWesternAsia	SubRegionWesternEurope	Year1991	Year1992	Year1993	Year1994	Year1995	Year1996	Year1997	Year1998	Year1999	Year2000	Year2001	Year2002	Year2003	Year2004	Year2005	Year2006	Year2007	Year2008	Year2009	Year2010	Year2011	Year2012	Year2013	Year2014	Year2015	Year2016	Year2017
987	8010	5074	3170	9188	2516	5949	2997	2662	5201	3917	3613	5952	1951	6051	7192	3955	5204	7232	9195	9704	5774	1.93	1.94	1.95	1.96	1.99	1.99	1.99	1.99	1.99	2.02	2.02	2.05	2.05	2.06	2.07	2.08	2.09	2.11	2.1	2.11	2.12	2.12	2.13	2.13	2.11	2.1	2.11	6800	3922	2144	5695	2121	4771	2285	2122	3486	2952	3717	5922	1587	4473	5704	3051	3458	6390	5730	8125	5967

Figure XX: VIF of lm(log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita)*Year.
log(gdp.per.capita)	log(gdp.per.capita):Year1991	log(gdp.per.capita):Year1992	log(gdp.per.capita):Year1993	log(gdp.per.capita):Year1994	log(gdp.per.capita):Year1995	log(gdp.per.capita):Year1996	log(gdp.per.capita):Year1997	log(gdp.per.capita):Year1998	log(gdp.per.capita):Year1999	log(gdp.per.capita):Year2000	log(gdp.per.capita):Year2001	log(gdp.per.capita):Year2002	log(gdp.per.capita):Year2003	log(gdp.per.capita):Year2004	log(gdp.per.capita):Year2005	log(gdp.per.capita):Year2006	log(gdp.per.capita):Year2007	log(gdp.per.capita):Year2008	log(gdp.per.capita):Year2009	log(gdp.per.capita):Year2010	log(gdp.per.capita):Year2011	log(gdp.per.capita):Year2012	log(gdp.per.capita):Year2013	log(gdp.per.capita):Year2014	log(gdp.per.capita):Year2015	log(gdp.per.capita):Year2016	log(gdp.per.capita):Year2017	Year1991	Year1992	Year1993	Year1994	Year1995	Year1996	Year1997	Year1998	Year1999	Year2000	Year2001	Year2002	Year2003	Year2004	Year2005	Year2006	Year2007	Year2008	Year2009	Year2010	Year2011	Year2012	Year2013	Year2014	Year2015	Year2016	Year2017
34.7	187	179	181	177	183	185	186	185	183	185	186	187	187	189	191	194	197	202	209	213	216	219	221	223	224	222	222	187	180	181	177	184	187	189	187	185	187	188	190	192	196	200	205	210	217	223	228	232	236	239	240	240	238	238

Although adding more features into our regression model results in higher R² values, the Variance Inflation Factor (VIF) for each are extremely high so we will reject those models as those added features are highly correlated with each other. Therefore, we will stick with our second model fit2.

We can then predict a country’s deaths caused from air pollution in a given year by using the country’s GDP per capita with the following equation:

\[ log(Deaths_{from~air~pollution|per~year|per~country} / 100,000) = 10.07849 - 0.38952 * log(GDP_{per capita}) ~~~~~~~~~~~~~~~~ eqn (1) \]

or solving for our target variable:

\[ Deaths_{from~air~pollution|per~year|per~country} = 10^{10.07849 - 0.38952 * log(GDP per capita)} * 100,000 ~~~~~~~~~~~~~~~~ eqn (2) \]

Is there a difference in means of death caused by pollution between low, mid, and high GDP per capita?

We all know that correlation does not necessarily mean causation. Let us dig a little deeper and test if means of deaths caused by air pollution per 100k across different GDP per capita levels are equal or not.

One-Way ANOVA Test

We start off by performing a One-Way ANOVA test to determine if the means of deaths caused by air pollution per 100k across different GDP per capita levels are equal or not.

H₀: $\mu$_{deaths_lowest_gdp} = $\mu$_{deaths_low_gdp} = $\mu$_{deaths_medium_gdp} = $\mu$_{deaths_high_gdp}

H₁: At least one of $\mu$_{deaths_lowest_gdp}, $\mu$_{deaths_low_gdp}, $\mu$_{deaths_medium_gdp}, $\mu$_{deaths_high_gdp} is not equal

We will sse an $\alpha$ value of 0.05.

The p-value_test1 is 0e+00, which is lower than $\alpha$_0.05. Therefore, we reject our null hypothesis that $\mu$_{deaths_lowest_gdp} = $\mu$_{deaths_low_gdp} = $\mu$_{deaths_medium_gdp} = $\mu$_{deaths_high_gdp}. This means that there is statistically significant that at least one of the means of deaths in low, medium, and high GDP per capita are not the same.

2-Sample T-Tests

We will conduct 6 2-sample t-tests to determine if each of the groupings are different from each other:

Lowest GDP per capita’s deaths does not equal Low GDP per capita’s deaths
- H₀: $\mu$_{deaths_lowest_gdp} = $\mu$_{deaths_low_gdp}
- H₁: $\mu$_{deaths_lowest_gdp} != $\mu$_{deaths_low_gdp}
Low GDP per capita’s deaths does not equal Medium GDP per capita’s deaths
- H₀: $\mu$_{deaths_low_gdp} = $\mu$_{deaths_medium_gdp}
- H₁: $\mu$_{deaths_low_gdp} != $\mu$_{deaths_medium_gdp}
Medium GDP per capita’s deaths does not equal High GDP per capita’s deaths
- H₀: $\mu$_{deaths_medium_gdp} = $\mu$_{deaths_high_gdp}
- H₁: $\mu$_{deaths_medium_gdp} != $\mu$_{deaths_high_gdp}
Lowest GDP per capita’s deaths does not equal High GDP per capita’s deaths
- H₀: $\mu$_{deaths_lowest_gdp} = $\mu$_{deaths_high_gdp}
- H₁: $\mu$_{deaths_lowest_gdp} != $\mu$_{deaths_high_gdp}
Lowest GDP per capita’s deaths does not equal Medium GDP per capita’s deaths
- H₀: $\mu$_{deaths_lowest_gdp} = $\mu$_{deaths_medium_gdp}
- H₁: $\mu$_{deaths_lowest_gdp} != $\mu$_{deaths_medium_gdp}
Low GDP per capita’s deaths does not equal Highest GDP per capita’s deaths
- H₀: $\mu$_{deaths_low_gdp} = $\mu$_{deaths_high_gdp}
- H₁: $\mu$_{deaths_low_gdp} != $\mu$_{deaths_high_gdp}

We will use a two sample t-test for each and use an $\alpha$ value of 0.05.

Test 1:

p-value_test1: 2.99e-203

p-value_test1 < $\alpha$_0.05 = TRUE

Conclusion of test1: p-value_test1 is less than $\alpha$_0.05, therefore we reject our null hypothesis that $\mu$_{deaths_lowest_gdp} is equal to $\mu$_{deaths_low_gdp} and accept our alternative hypothesis.

Test 2:

p-value_test2: 1.47e-13

p-value_test2 < $\alpha$_0.05 = TRUE

Conclusion of test2: p-value_test2 is less than $\alpha$_0.05, therefore we reject our null hypothesis that $\mu$_{deaths_low_gdp} is equal to $\mu$_{deaths_medium_gdp} and accept our alternative hypothesis.

Test 3:

p-value_test3: 0e+00

p-value_test3 < $\alpha$_0.05 = TRUE

Conclusion of test3: p-value_test3 is less than $\alpha$_0.05, therefore we reject our null hypothesis that $\mu$_{deaths_medium_gdp} is equal to $\mu$_{deaths_high_gdp} and accept our alternative hypothesis.

Test 4:

p-value_test4: 2.91e-06

p-value_test4 < $\alpha$_0.05 = TRUE

Conclusion of test4: p-value_test4 is less than $\alpha$_0.05, therefore we reject our null hypothesis that $\mu$_{deaths_lowest_gdp} is equal to $\mu$_{deaths_high_gdp} and accept our alternative hypothesis.

Test 5:

p-value_test5: 4.79e-48

p-value_test5 < $\alpha$_0.05 = TRUE

Conclusion of test5: p-value_test5 is less than $\alpha$_0.05, therefore we reject our null hypothesis that $\mu$_{deaths_lowest_gdp} is equal to $\mu$_{deaths_medium_gdp} and accept our alternative hypothesis.

Test 6:

p-value_test6: 4.17e-70

p-value_test6 < $\alpha$_0.05 = TRUE

Conclusion of test6: p-value_test6 is less than $\alpha$_0.05, therefore we reject our null hypothesis that $\mu$_{deaths_low_gdp} is equal to $\mu$_{deaths_high_gdp} and accept our alternative hypothesis.

6. Conclusion

Main Research Results

From all of our tests, we can confirm that the means of deaths caused by air pollution are statistically significant when grouped by different levels of GDP per capita. This reinforces the idea that deaths caused by air pollution has a significant relationship with GDP per capita and the model can be quantified by Equation 2:

\[ Deaths_{from~air~pollution|per~year|per~country} = 10^{10.07849 - 0.38952 * log(GDP per capita)} * 100,000 ~~~~~~~~~~~~~~~~ eqn (2) \]

The strength of the correlation can be quantified by our R² value of 0.737 from Figure XX.

Areas of Further Analysis

This data set has many avenues for further statistical analysis and modeling. Some potential areas for further analysis include:

Can we quantify or create a mathematical model of what GDP per capita value reaches the asymptotic relationship we observed in the log data set?
Can we build a better performing predictor for Deaths per 100k due to Air Pollution using more powerful models (Random Forests, Gradient Boosting, SVMs) and/or by including more features?

7. Bibliography

Figure X: References
Number	APA Citation
1	Robin Lovelace, J. N. (n.d.). Chapter 8 Making maps with R: Geocomputation with R. Retrieved October 28, 2021, from https://geocompr.robinlovelace.net/adv-map.html
2	Robin Lovelace, J. N. (2021, October 28). Chapter 2 Geographic data in R: Geocomputation with R. Retrieved from https://geocompr.robinlovelace.net/spatial-class.html#intro-sf
3	Hadley Wickham, D. N. (2021, October 28). 6 Maps. Retrieved from https://ggplot2-book.org/maps.html
4	Customizing ggplot2 color and fill scales. (2021, October 28). Retrieved from https://spielmanlab.github.io/introverse/articles/color_fill_scales.html
5	Logarithmic Functions. (2021, October 28). Retrieved from https://saylordotorg.github.io/text_intermediate-algebra/s10-03-logarithmic-functions-and-thei.html